South Australian Liberal senator Cory Bernardi has urged the Foreign Minister not to endorse a "dysfunctional", "vengeful", "unstable", "megalomaniac" like former prime minister Kevin Rudd for the United Nations top job.

It comes amid speculation Mr Rudd will nominate to become the next secretary-general, despite it being revealed former prime minister Tony Abbott gave a commitment to his New Zealand counterpart John Key that Australia would support his predecessor Helen Clark.

"As prime minister, Mr Rudd brought an unprecedented level of dysfunction and chaos to Australian politics and to the position of prime minister."

Senator Bernardi was not afraid to use strong language to press his point to Ms Bishop.

"His own colleagues have described him as a 'megalomaniac', 'vengeful', 'unstable' and 'a bastard' with a 'vicious temper' who put 'his own self-interest ahead of … the country as a whole'," Senator Bernardi wrote.

"Similar sentiments were expressed by many of our Coalition colleagues on multiple occasions over many years.

"It is my considered view that our own supporters and many others in the Australian public would be very disappointed if we endorsed such a person for this significant role.

"Would you be kind enough to advise me if the Government is seriously considering this course of action and if so, please provide me with the rationale for such a position."

Senator Bernardi told the ABC he was not sure whether Mr Rudd was a "real chance or not" to replace current secretary-general Ban Ki-Moon.

"But I think for us to sponsor someone of such character traits when we've been complaining about him and reminding people about that for many, many years, really doesn't reflect well on us," Senator Bernardi said.

"Unless of course ... the plan is to destroy the United Nations from within, then that's what I think he would do."

Ms Bishop said it would be up to Cabinet to decide which candidate to back.

In a statement, Mr Rudd's office responded to Senator Bernardi's character assessment and told the ABC he was not a candidate to become secretary-general.

"Mr Rudd is the president of the Asia Society Policy Institute, which is a full-time position," a spokeswoman said.

"Based on the long-entrenched UN geographical rotational system, the next UNSG will be from Eastern Europe.